You're asking about what is generally referred to as the "joint-participant exception."
In the United States, the answer varies from jurisdiction to jurisdiction, as each state sets its own rules on which communications are privileged and which are not. Even in the federal courts, where the law should be relatively consistent, there is some disagreement on this question.
After the Tenth Circuit recognized the exception in Trammel v. United States, 445 U.S. 40, (1980), the Supreme Court gave a vague statement suggesting that the exception does not exist, but it was not clear enough to settle the question.
Since then, the Seventh Circuit has said the exception applies, but the First, Second, Third, and Ninth circuits have said it does not. So until the Supreme Court weighs in again, the answer is "it depends where you live."
Keep in mind also that what is often referred to as "spousal privilege" actually encompasses two very distinct privileges: (1) the spousal communications privilege, which is a defendant's right to block testimony about his statements to his spouse; and (2) the spousal testimonial privilege, which is a witness's right to refuse to testify against his spouse. It may be that in some jurisdictions, the joint-participant exception applies to one but not the other.